IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v129y2014icp193-205.html
   My bibliography  Save this article

Jackknife empirical likelihood inference with regression imputation and survey data

Author

Listed:
  • Zhong, Ping-Shou
  • Chen, Sixia

Abstract

We propose jackknife empirical likelihood (EL) methods for constructing confidence intervals of mean with regression imputation that allows ignorable or nonignorable missingness. The confidence interval is constructed based on the adjusted jackknife pseudo-values (Rao and Shao, 1992). The proposed EL ratios evaluated at the true value converge to the standard chi-square distribution under both missing mechanisms for simple random sampling. Thus the EL can be applied to construct a Wilks type confidence interval without any secondary estimation. We then extend the proposed method to accommodate Poisson sampling design in survey sampling. The proposed methods are compared with some existing methods in simulation studies. We also apply the proposed method to an Italy household income panel survey data set.

Suggested Citation

  • Zhong, Ping-Shou & Chen, Sixia, 2014. "Jackknife empirical likelihood inference with regression imputation and survey data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 193-205.
    • Handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:193-205
    DOI: 10.1016/j.jmva.2014.04.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14000931
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.04.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. Jae Kwang Kim & Jongho Im, 2014. "Propensity score adjustment with several follow-ups," Biometrika, Biometrika Trust, vol. 101(2), pages 439-448.
    3. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
    4. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    5. Qin, Jing & Zhang, Biao & Leung, Denis H. Y., 2009. "Empirical Likelihood in Missing Data Problems," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1492-1503.
    6. Jae Kwang Kim, 2011. "Parametric fractional imputation for missing data analysis," Biometrika, Biometrika Trust, vol. 98(1), pages 119-132.
    7. Yang, Hanfang & Zhao, Yichuan, 2013. "Smoothed jackknife empirical likelihood inference for the difference of ROC curves," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 270-284.
    8. Kim, Jae Kwang & Yu, Cindy Long, 2011. "A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 157-165.
    9. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
    10. Jae Kwang Kim, 2004. "Fractional hot deck imputation," Biometrika, Biometrika Trust, vol. 91(3), pages 559-578, September.
    11. Cheng Yong Tang & Yongsong Qin, 2012. "An efficient empirical likelihood approach for estimating equations with missing data," Biometrika, Biometrika Trust, vol. 99(4), pages 1001-1007.
    12. Chen J. & Shao J., 2001. "Jackknife Variance Estimation for Nearest-Neighbor Imputation," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 260-269, March.
    13. Wayne A. Fuller, 2009. "Some design properties of a rejective sampling procedure," Biometrika, Biometrika Trust, vol. 96(4), pages 933-944.
    14. Song Chen & Ingrid Van Keilegom, 2009. "Rejoinder on: A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 468-474, November.
    15. Song Xi Chen & Denis H. Y. Leung & Jing Qin, 2008. "Improving semiparametric estimation by using surrogate data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 803-823, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Dec 2023.
    2. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," STICERD - Econometrics Paper Series 617, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Heng Wang & Ping-Shou Zhong, 2017. "Order-restricted inference for means with missing values," Biometrics, The International Biometric Society, vol. 73(3), pages 972-980, September.
    4. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Zhang, Xiuzhen & Lu, Zhiping & Wang, Yangye & Zhang, Riquan, 2020. "Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    6. Zhong Guan & Jing Qin, 2017. "Empirical likelihood method for non-ignorable missing data problems," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 113-135, January.
    7. Guo, Xu & Song, Lianlian & Fang, Yun & Zhu, Lixing, 2019. "Model checking for general linear regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 1-12.
    8. Chen, Sixia & Haziza, David, 2018. "Jackknife empirical likelihood method for multiply robust estimation with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 258-268.
    9. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.
    10. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    2. Hui-Ling Lin & Zhouping Li & Dongliang Wang & Yichuan Zhao, 2017. "Jackknife empirical likelihood for the error variance in linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 151-166, April.
    3. Yves G. Berger, 2020. "An empirical likelihood approach under cluster sampling with missing observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 91-121, February.
    4. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    5. Zhang, Jia & Shi, Haoming & Tian, Lemeng & Xiao, Fengjun, 2019. "Penalized generalized empirical likelihood in high-dimensional weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 270-283.
    6. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    7. Li, Minqiang & Peng, Liang & Qi, Yongcheng, 2011. "Reduce computation in profile empirical likelihood method," MPRA Paper 33744, University Library of Munich, Germany.
    8. Zhang, Rongmao & Peng, Liang & Qi, Yongcheng, 2012. "Jackknife-blockwise empirical likelihood methods under dependence," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 56-72, February.
    9. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    10. Bravo, Francesco & Escanciano, Juan Carlos & Van Keilegom, Ingrid, 2015. "Wilks' Phenomenon in Two-Step Semiparametric Empirical Likelihood Inference," LIDAM Discussion Papers ISBA 2015016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Zang, Yangguang & Zhang, Sanguo & Li, Qizhai & Zhang, Qingzhao, 2016. "Jackknife empirical likelihood test for high-dimensional regression coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 302-316.
    12. Yves G. Berger & Ewa Kabzińska, 2020. "Empirical Likelihood Approach for Aligning Information from Multiple Surveys," International Statistical Review, International Statistical Institute, vol. 88(1), pages 54-74, April.
    13. Hong Guo & Changliang Zou & Zhaojun Wang & Bin Chen, 2014. "Empirical likelihood for high-dimensional linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 921-945, October.
    14. Zhong Guan & Jing Qin, 2017. "Empirical likelihood method for non-ignorable missing data problems," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 113-135, January.
    15. Chen, Sixia & Haziza, David, 2018. "Jackknife empirical likelihood method for multiply robust estimation with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 258-268.
    16. Yu Shen & Han-Ying Liang, 2018. "Quantile regression and its empirical likelihood with missing response at random," Statistical Papers, Springer, vol. 59(2), pages 685-707, June.
    17. Shu Yang & Jae Kwang Kim, 2016. "Likelihood-based Inference with Missing Data Under Missing-at-Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 436-454, June.
    18. Chen, Sixia & Haziza, David, 2023. "A unified framework of multiply robust estimation approaches for handling incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    19. Weihua Zhao & Riquan Zhang & Yukun Liu & Jicai Liu, 2015. "Empirical likelihood based modal regression," Statistical Papers, Springer, vol. 56(2), pages 411-430, May.
    20. Sanjay Chaudhuri & Debashis Mondal & Teng Yin, 2017. "Hamiltonian Monte Carlo sampling in Bayesian empirical likelihood computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 293-320, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:193-205. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.